Abstract
The material point method (MPM) has been widely used in a broad area of engineering. However, it still suffers from the accuracy problem. One of the most important sources of the accuracy problem is the error of particle quadrature. The discontinuity of the gradient of the shape function causes severe crossing-mesh error. This paper proposes a new transport point method (TPM) which employs a mixed quadrature scheme combining Gaussian quadrature in the internal cells and particle quadrature in the boundary cells. The main distinction between the TPM and MPM is the quantities carried by particles. The transport points in TPM do not have volume and only carry intensive quantities and have dual properties of both Euler and Lagrange. The MLS method is used to reconstruct quantities at cell centers and nodes, and the integral weight is the cell volume. A point rearrangement algorithm is proposed so that the transport points can be added, moved or deleted arbitrarily as long as the accuracy of the reconstructed flow field is maintained, which can be used to eliminate the numerical fracture and impose inlet condition.
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